Mathematical Logic

Research Activity

The interests of our members cover a broad spectrum of computability theory, proof theory, reverse mathematics, and algorithmic randomness, and their applications.

Research in computability theory deals with algebraic characterizations of the computational power of programs using oracles (e.g., interactive computing). The primary structures which are studied are the degrees of unsolvability and its substructures, such as the computably enumerable degrees.

The construction of computable models for algebraic and combinatorial structures is studied in the area of computable model theory.

Reverse mathematics classifies theorems of mathematics according to the weakest axioms needed to prove them.